Factoring an infinite abelian group by lacunary cyclic subsets

Abstract

It was proved in Corradi and Szabo (Math Pannonica 5:275–280, 1994) that if a finite abelian group of odd order is factored into a direct product of lacunary cyclic subsets, then at least one of the factors must be a subgroup. The paper extends this result for certain infinite torsion groups.